Let Q=$\frac{(sin2x+b)(2sinx-1)}{a^2-4tanx}$,where x =45$^{\circ}$. a=18 and b =$\sqrt{2}$.
1.Find the exact value of Q.
Q=  .
2.Give your answer to part (a) correct to

2.1.three decimal places;
The number is   .
2.2.three significant figures.
The number is   .
3.Calculate the percentage error if Q is given to three decimal places.
Using the percentage error formula ϵ=  %

  The distance between two points ah n x:i jfe5ros8,c.-with coordinates (x$_1$,y$_1$) and (x$_2$,y$_2$) is equal to
$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
1.Calculate the distance between points A(40,−100) and B(1,−2). Give your answer correct to three significant figures.
The distance between points A(40,−100) and B(1,−2) is AB≈  .
2.Give your answer from part (a) correct to one decimal place.The number=  .

3.Write the answer to part (b) in the form a×10$^k$, where 1≤a<10, k∈Z.The number=  ×104$^2$

  Let F=$\frac{(4sin2z-1)(2tan3z+1)}{x^2-y^2}$,where x=12, y=8 and z=15°.

1.Calculate the exact value of F.
F=  .
2.Give your answer to F correct to

2.1.two significant figures;The number=  .

2.2.two decimal places.The number=  .

Sasha estimates the value of F to be 0.03.

3.Calculate the percentage error in Sasha's estimate.the percentage=  %.

  
1.Find the value of A. Write down your full calculator display.
A=  .
2.Give your answer to part (a) correct to

2.1.three significant figures;
The number=  .
2.2.three decimal places.
The number=  .
3.Give the answer to part (b) (i) in the form a×10$^k$, where 1≤a<10, k∈Z.
The number=  ×10$^{-2}$.

  A cuboid has the followiil,*e/ snn:m3 w)ddpcng dimensions: length=9.6 cm, width=7.4 cm, and height=5. ):/ni s3*d ,pmwcledn2 cm.

1.Calculate the exact value of the volume of the cuboid, in cm$^3$
V=  cm$^3$.
2.Write your answer to part (a) correct to

2.1.two decimal places;
The number=  .
2.2.three significant figures.
The number=  .
3.Write your answer to part (b) (ii) in the form a×10$^k$ , where 1≤a<10 and k∈Z.The number=  ×10$^2$.

  Four cement bags labelled, "5 kg", were delivered toiy jq ,lgjfx2t8*e 5,1urc-gc a customer. The customer measured ,t ju5-y,l2 q fxc1c egrij*8geach bag to check their weights and recorded the following:

4.92,4.95,5.02,4.95
​
1.1.Find the mean of the customer's measurements.
If we calculate the mean of the measurements, we get μ=  .
1.2.Calculate the percentage error between the mean and the stated,
approximate weight of 5 kg.
Using the percentage error formula ϵ=  %.

2.1.correct to the nearest integer;
The number=  .
2.2.in the form a×10$^k$, where 1≤a<10 and k∈Z.
The number=  ×10$^1$.

  After solving a problem, John has an exacvf43fkj 4nav1 t answer of z=0.1475.

1.Write down the exact value of z in the form a×10$^k$ , where 1≤a<10,k∈Z.
The number=  ×10$^{-1}$.
2.State the value of z given correct to 2 significant figures.
The number=  .
3.Calculate the percentage error if z is given correct to 2 significant figures.
Using the percentage error formula ϵ=  %.

  Given that z=$\frac{10sina}{3x+y}$,where α=30°, x=6 and y=46.
1.Find the exact value of z. z=  .

2.Write your answer to part (a)

2.1.correct to 2 decimal places;
The number=  .
2.2.correct to 3 significant figures;
The number=  .
2.3.in the form a×10$^k$ , where 1≤a<10 and k∈Z.
The number=  ×10$^{-2}$.

  The following diagram shows a rectangle with sides of length 7*ad dd8 .m67-d.biy et5zhy(to eux6 m.6×10$^2$cm and 1.5×10$^3$cm.

1.Write down the area of the rectangle in the form a×10$^k$ , where1≤a<10 and k∈Z.

Natalie estimates the area of the rectangle to be 1200000 cm.
A=  ×10$^6$

2.Find the percentage error in Natalie's estimate.
Using the percentage error formula ϵ=  %

  The volume of a hemisphere, V, is giv- zcpggsz5 pg s, j,,ig:al+h0en by the formula

where S is the total surface area.

The total surface area of a given hemisphere is 529 cm$^2$.

1.Calculate the volume of this hemisphere in cm$^3$ . Give your answer correct to one decimal place.
V=  cm$^3$
2.Write down your answer to part (a) correct to the nearest integer.
The number=  cm$^3$.
3.Write down your answer to part (b) in the form a×10$^k$ , where 1≤a<10 and k∈Z.
The number=  ×10$^2$ cm$^3$.

  
1.calculate the value of r.
r=  .
Albert first writes a, b and c correct to one significant figure and then uses these values to estimate the value of r.

2.1.Write down a, b and c each correct to one significant figure.
a=  ,b=  ,c=  .
2.2.Find Albert's estimate of the value of r.
r=  .
3.Calculate the percentage error in Albert's estimate of the value of r.
Using the percentage error formula ϵ=  %.